Answer: To find the value of g(2+h)-g(2) divided by h, we can use the definition of the derivative. The derivative of a function at a point is a measure of the slope of the function at that point, and it can be calculated by taking the limit of the difference quotient as h approaches 0.
The difference quotient is defined as:
[g(2+h) - g(2)] / h
So, to find the derivative of g at x=2, we can substitute the value of x in the function g(x) and take the limit as h approaches 0:
lim h→0 [g(2+h) - g(2)] / h
Substituting the value of x in the function g(x), we get:
lim h→0 [(2+h)³ - 2(2+h) - (2² - 2*2)] / h
This simplifies to:
lim h→0 [8+6h+h²-2h - 4] / h
Which simplifies to:
lim h→0 [h²+6h+4] / h
And, finally:
lim h→0 [h(h+6)] / h
The limit of a quotient is equal to the quotient of the limits, as long as the limit of the denominator is not 0. In this case, the limit of the denominator (h) is 0, but the limit of the numerator (h(h+6)) is not. Therefore, we can safely take the limit:
h+6
So, the derivative of g at x=2 is h+6. When h=0, the derivative is equal to the function's value at that point, so the value of g(2) is 6.
Therefore, the value of g(2+h)-g(2) divided by h is:
(h+6) - 6 / h
Which simplifies to:
h / h
Which is equal to:
1
So, the final answer is 1.
Step-by-step explanation:
the quotient of x divided by 5 is greater than or equal to 6. Write an inequality and graph its solution
The side of a triangle are 64, 47 And 39 use the Pythagorean theorem to determine if a triangle is right acute or obtuse
Answer: obtuse
Step-by-step explanation:
64+47=111
111>39
correct 0.00798516 to three significant figures
Explanation:
The zeros in 0.00798516 are not considered significant because they are not between nonzero values.
If we had something like 1.207, then that zero would be considered significant.
The first three significant values we come across in 0.00798516 are 7, 9 and 8 in that order. The next digit 5 meets the criteria of "5 or larger", which means the 798 bumps up to 799. Erase everything to the right of that.
Therefore, 0.00798516 rounds to 0.00799 when rounding to 3 significant figures.
Answer: 0.00799
0.00798516 rounded off to three significant figures is 0.00799
hope that helps...
100° хо 100%
what is the answer for x?
The answer of x is 100 degree.We can find by using percentage formula.
What do we mean by percentage?Percentage is a value or ratio that shows a fraction of 100. Percent means per 100. It does not have any units.If we have to calculate percent of a number then we divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”.
What is the percentage formula?The formula used to calculate percentage is: (value/total value)×100%.The most basic application of percentages is to compare one quantity against another. When we want to talk about data in this way we use it with the word, "of." To use this data as an example, we would say, for example, "25% of people prefer cake," as in this example.
Now we have
100 = x of 100%
100= x * 100/100
100= x
Hence we can calculate value of x.
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(2x+1)(x-3)(x+5) expand and fully simplify
Answer:
2x^3+5x^2−28x−15
Step-by-step explanation:
(16,1), (17,7) find the slope of line through each pair of points
The slope of the line through each pair of points (16,1), (17,7) is 6.
A line's slope serves as a gauge for its steepness. Between any two locations on the line, it is the ratio of the vertical change to the horizontal change.
The slope of a line can be positive, negative, zero, or undefined.
In algebraic equations, the letter "m" frequently stands in for slope. In slope-intercept form, a line's equation is written as y = mx + b, where m denotes the line's slope and b its y-intercept.
To find the slope of the line that passes through two points (x1, y1) and (x2, y2), you can use the following formula
m = (y2 - y1) ÷ (x2 - x1)
where m is the slope of the line and (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, the slope of the line through the points (16,1) and (17,7) is:
m = (7 - 1) ÷ (17 - 16) = 6 ÷ 1 = 6
So the slope of the line is 6.
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Mike went on a bicycle trip. Every 4 days he travels 230 miles.
Create a proportional table comparing miles traveled to days spent traveling.
Calculating the ratio between each pair of values in a table allows you to determine whether a proportional relationship is present. The table depicts a proportional relationship if all of those ratios are the same.
How should an equation for a proportional table be written?y = k x, where is the proportionality constant, is the equation that depicts a proportional relationship, or a line. Find k and create the equation by using k = y x from a table or graph. Tables, graphs, and equations can all be used to depict proportional relationships.
How should a proportional relationship be written?The equation y = kx represents a proportional relationship between two quantities y and x that have the same proportionality constant, k.
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a parking lot contains only cars and motor bikes. if there are 18 vehicles and 50 tires in the parking lot, how many cars and bikes are there?
Answer:
Step-by-Step:5 cars and 14 bikes
A quantity with an initial value of 800 grows continuously at a rate of 4.5% per year. What is the value of the quantity after 96 months, to the nearest hundredth?
The value of the quantity after 96 months, to the nearest hundredth is 1146.66
Exponential equationsThe standard expression for an exponential equation is expressed as:
P(t) = P0e^rt
Given the following parameters
Po = 800
rate r = 4.5% = 0.045
time t = 8 years
Substitute
P(8) = 800e^0.045(8)
P(8) = 1146.66
Hence the value of the quantity after 96 months, to the nearest hundredth is 1146.66
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Katrina buys a 76-ft roll of fencing to make a rectangular play area for her dogs. Use
2({+w) = 76 to write a function for the length, given the width. Graph the function.
What is a reasonable domain for the situation? Explain.
Therefore , As a result 5, 10, and 15 make up the reasonable domain for the function 2 (l + w) = 64..
The definition of functionA connection between a group of sources and one output for each input is referred to as a function. A function is, to put it simply, a collection of equation connected to a single, unique output. In mathematics, a function is a statement, rule, or law that describes the connection between two variables (the dependent variable). One input leads to one output when a rule of this type is used. by Alex Federspiel, the photographer. This statement gives an example of y=x2. There is just one output for y from any input for x. According to our definition, y is a function of x since x is the input value.
Here,
We have the following for the rectangle's perimeter:
2 ( l + w ) = 64
Here,
W = width, and L = length.
We must determine the length and breadth values necessary to make the rectangle's perimeter 64.
Now,
2 ( l + w ) = 64
l + w = 32
Thus, the sum of the length and breadth measurements must equal 32.
The possible widths are 5, 10, 15, 20, and 25.
Now,
l + 5 = 32
l = 27
l + 10 = 32
l = 22
l + 15 = 32
l = 17
l + 20 = 32
l = 12
l + 25 = 32
l = 7
We think about
The domain has widths of 5, 10, 15, 20, and 25.
The range for length is: 27, 22, 17, 12, and 7.
Values for width and length are used as the x- and y-axes, respectively.
Below is a graph of the data.
The following is the reasonable domain for the aforementioned situation:
5, 10, 15, 20, and 25
Below is a graph of the function 2 (l + w) = 64.
Therefore , As a result, 5, 10, and 15 make up the reasonable domain for the function 2 (l + w) = 64.
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50 POINTS !!
PLEASE HELP !! ILL GIVE BRAINLIEST TO THE RIGHT ANSWERS.
Hi there!
[tex]\large\boxed{35 \text{ units}^2}[/tex]
Find the area of the parallelogram using the formula:
A = b × h
Thus:
A = 7 × 5 = 35 units²
Answer:
Step-by-step explanation:
I believe that the answer is 85
Equation of Exponential Functions
The table of values below represent an exponential function.
Write an exponential equation that models the data.
a. y = 11.76(1.3)× c. y = 11.76(0.7)×
b. y = 24(07)× d. y = 16.8(1.7)×
Please select the best answer from the choices provided.
Answer:
C. y = 11.76(0.7)×
Step-by-step explanation:
I calculated it logically
The exponential equation that models the data is y = 16.8×1.7ˣ.
What is a function?A relation is a function if it has only One y-value for each x-value.
y = a.rˣ is the exponential function.
We can see that the y-values are decreasing, which means that the growth factor must be between 0 and 1.
Additionally, we can divide the y-value for each x by the y-value for the previous x to get an estimate of the growth factor.
Using this method, we find that the growth factor is approximately 0.85, which means that a possible equation is y = a × 0.85ˣ.
To find the value of a, we can substitute one of the data points into the equation.
Lets use the point (-2, 24), we get:
24 = a × 0.85⁻²
a = 24 / 1.551
a = 15.456
Therefore, the exponential equation that models the data is y = 16.8×1.7ˣ.
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The equation of the line passing through the points (−1, 2) and (4, 0) is given by ax + by = 16. What is the value of b?
Answer:
8/5
Step-by-step explanation:
Slope of the line = (-1-4)/(2-0)= -5/2
Equation of the line :
=> y - y1 = m(x - x1)
=> y - 0 = (-5/2)(x - 4)
=> 2(y - 0) = - 5x + 20
=> 2y + 5x = 20
To make the RHS 16, divide both sides by 20 and multiply by 16:
=> (2y/20)*16 + (5x/20)*16 = (20/20)*16
=> 8y/5 + 4x = 16
compare the equation with ax + by = 16 for y, b = 8/5
What is the differences between solving an equation and solving an inequality?
The equation includes equal to sign and the inequality includes the sign of greater than and equal to sign.
What is inequality?Inequality is defined as the relation which makes a non-equal comparison between two given functions.
when we have to solve an equation, it does not has an equal sign and inequalities.
When we have to solve an inequality equations usually are exact answers.
The equation includes equal to sign and the inequality includes the sign of greater than and equal to sign.
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1) A publisher wants to determine the thickness of a book they will print soon. The book has a front cover and a back cover, each of which have a thickness of
1/4 in. The publisher can choose on what type of paper to print the book.
Bond paper has a thickness of 1/4 in. per 100 pages.
Write an equation that gives the width `y` of the book, if it has `x`-hundred pages printed on bond paper.
Ledger paper has a thickness of 2/5 in. per `100` pages. Write an equation that gives the width `y` of the book, if it has `x`-hundred pages printed on ledger paper.
2) If the publisher selects front and back covers with a thickness of 1/3 in. each, how would this change the equations you wrote on the previous slides?
1a) An equation that gives the width `y` of the book, if it has `x`-hundred pages printed on bond paper is; y = ¹/₂ + ¹/₄x
1b) Ledger paper has a thickness of 2/5 in. per `100` pages, the equation is; y = ¹/₂ + ²/₅x
2) The equation will be; y = ²/₃ +¹/₄x
How to solve Algebraic Word Problems?1) We are told that the front cover and the back cover have a thickness of 1/4 inches and they also have a thickness of 1/4 inch. Thus;
The addition of both gives to the book thickness of;
1/4 + 1/4 = 1/2 inch, despite how many pages the book has.
We are told that for every hundred pages, a thickness of 1/4 inch is added to the book, then the equation is:
y = ¹/₂ + ¹/₄x
where;
y is the width of the book in inches.
x is every hundred pages printed on bond paper.
1b) If ledger paper has a thickness of 2/5 in. per 100 pages, then the equation is now;
y = ¹/₂ + ²/₅x
2) If both front and back covers now, have a thickness of 1/3 inches instead of 1/4 inches each, then the equation will be;
y = 2(1/3) +¹/₄x
y = ²/₃ +¹/₄x
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please please help me Please help for my math rpoject!!!!!
a. The table for the relation is given by the image shown at the end of the answer.
b. The domain and range of the relation are given as follows:
Domain: {0, 1, 2, 3, 4, ...}.Range: {0, 0.75, 1.5, 2.25, ...}.c. The relation is a function, as it value of the input is mapped to a single value of the output.
How to represent the situation?The ratio between the total cost and the number of vehicles is obtained as follows:
k = 3.75/5 = 3/4 = ... = 0.75/1 = 0.75.
Meaning that the situation is modeled by a proportional relationship with a constant of 0.75, and the function is given as follows:
y = 0.75x.
For which:
x is the number of cars.y is the total cost.The domain and range are given as follows:
Domain: {0, 1, 2, 3, 4, ...}. -> possible amounts of cars.Range: {0, 0.75, 1.5, 2.25, ...}. -> possible prices.More can be learned about proportional relationships at https://brainly.com/question/10424180
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Find the sum and express it in simplest form.
(7t³ + 3t - 1) + (-9t³ + 2t)
DO
Enter the correct answer.
Answer:
-2[tex]t^{3}[/tex] + 5t - 1
Step-by-step explanation:
(7[tex]t^{3}[/tex] + 3t - 1) + (-9[tex]t^{3}[/tex] + 2t)
7[tex]t^{3}[/tex] - 9[tex]t^{3}[/tex] + 3t + 2t - 1 Combine like terms
-2[tex]t^{3}[/tex] + 5t - 1
Like terms have to have the same variable and the same exponents to be like terms.
Todd caught at least three times as many fish this year than last year. He caught 63
fish this year. Which inequality represents how many fish he caught last year?
Answer:
3y ≥ 63
Step-by-step explanation:
Ill tell you how I did it hold on
Answer:
3y ≤ 63
Step-by-step explanation:
3y ≤ 63
y ≤ 21
this means that last year ('y') he caught, at most, 21 fish - this is 1/3 less than this year
8-2z+3(x+y), when x=4, y=9, Z=3
[tex]8-2z+3(x+y)[/tex] when x is 4, y is 9, and z is 3
Substitute:
[tex]8-2(3)+3(4+9)[/tex]
[tex]8-6+39[/tex]
Solve:
[tex]8-6+39\\=\fbox{23}[/tex]
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{8 - 2z + 3(x + y)}[/tex]
[tex]\mathsf{= 8 - 2(3) + 3(4 + 9)}[/tex]
[tex]\mathsf{= 8 - 6 + 3(4) + 3(9)}[/tex]
[tex]\mathsf{= 8 - 6 + 12 + 27}[/tex]
[tex]\mathsf{= 2 + 12 + 27}[/tex]
[tex]\mathsf{= 14 + 27}[/tex]
[tex]\mathsf{= 41}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{41}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
What is the solution to the system of equations graphed below?
wht is the answer ???
The equation to represent the height of a glass slab is y=11x+2.
What is the equation of a line?The general equation of a straight line is y=mx+c, where m is the gradient, and y = c is the value where the line cuts the y-axis. This number c is called the intercept on the y-axis.
From the given table, we have (2, 24) and (4, 46).
Substitute (x₁, y₁)=(2, 24) and (x₂, y₂)=(4, 46) in m=(y₂-y₁)/(x₂-x₁)
= (46-24)/(4-2)
= 22/2
= 11
Substitute m=11 and (x, y)=(2, 24) in y=mx+c, we get
24=11(2)+c
c=2
Substitute m=11 and c=2 in y=mx+c, we get
y=11x+2
Therefore, the equation to represent the height of a glass slab is y=11x+2.
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Which defines a line segment?
Answer: A line segment is a part of a line having two endpoints.
Im not sure if you meant to put a picture there. So, a line segment is a piece or part of a line having two endpoints. Unlike a line, a line segment has a definite length.
the cylindrical toothbrush holder modeled below has a diameter of 6.5 centimeters and a height of 9 centimeters. The shaded part represents the base of the cylinder.
A formula for finding the volume for a cylinder is V= Bh which equation can be used to find b, the area of the cylinders base in square centimeters?
A B= 3.14(6.5/2)^2
B B = 3.14(6.5/2)
C B = 3.14(6.5)^2
D B = 3.14(6.5)
Answer: B
Step-by-step explanation:
Two cars leave the same parking lot, with one heading north and the other heading'east. After several minutes, the northbound car has
traveled 12 kilometers and the eastbound car has traveled 9 kilometers, measured in a straight line. How far apart are the two cars? Round
to the nearest tenth, if a decimal.
Answer:
I DONT KNOW DO YOU?
In this case, how would it be resolved if it does not indicate any base, only brand X
The coordinates of the vertices of the square with height x is given as follows:
H(-x,x).I(0,x).J(0,0).K(-x,0).What is a square?A square is a figure for which all the four side lengths are congruent, that is, they have the same measure.
The side length of the square in this problem is given as follows:
x.
As the height is equals to the base.
The vertex J represents the origin, hence it has coordinates given as follows:
J(0,0).
Then the remaining coordinates of the square are given as follows:
H(-x,x). -> x units left and x units up from the origin.I(0,x). -> x units up from the origin.K(-x,0). -> x units left from the origin.More can be learned about squares at https://brainly.com/question/30179630
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Which of the following sets of ordered pairs represents a function?
OA. {(9,7), (0, -4), (8,4), (0,6) }
OB. {(0, 1), (0, -1), (2, 4), (5,6) }
OC. {(1, 8), (1, 0), (1, -8), (1, 1) }
OD. {(2,4), (0, 0), (4,8), (3,6)}
PLEASE HELP!! It takes Sheila 36 minutes to edit a commercial. How many commercials can
she edit in 144 minutes?
Answer:
she can edit 4 commericals in 144 minutes.
Step-by-step explanation:
144 divided by 36 is 4
Answer:
180
Step-by-step explanation:
you have to add 36/144 to get your answer our welcome.
Please Help ASAP I don't know this well
Answer:
Step-by-step explanation:
First of all I'm going to presume it means an eight-grader chosen at random from the instrument players, if this is incorrect the question should have specified the total amount of students.
You have to add the amount of students of each of instrument to get the total:
5+9+10+9=33
then it says to not include the drum playing students so it goes from
[tex]\frac{33}{33}[/tex] to [tex]\frac{33-10}{33}[/tex] so its [tex]\frac{23}{33}[/tex] which we must now turn to a percentage.
so you divide the 23 by the 33:
23/33=0.6969....
then you multiply by 100 as it's a percentage:
0.6969...×100=69.6969...
and finally we round it do the nearest integer/whole number:
70 (we look at the tenths digit and it's a 6 so it's rounded up)
In(3x2 - 1) = In(191)
Given:
The equation is:
[tex]\ln(3x^2-1)=\ln(191)[/tex]
To find:
The solution for the given equation.
Solution:
We have,
[tex]\ln(3x^2-1)=\ln(191)[/tex]
On comparing both sides, we get
[tex]3x^2-1=191[/tex]
[tex]3x^2=191+1[/tex]
[tex]3x^2=192[/tex]
Divide both sides by 3.
[tex]x^2=\dfrac{192}{3}[/tex]
[tex]x^2=64[/tex]
Taking square root on both sides, we get
[tex]x=\pm \sqrt{64}[/tex]
[tex]x=\pm 8[/tex]
Therefore, the solutions of the given equation are -8 and 8.
The diagram shows a circle with center C, a diameter RS, and an inscribed triangle RST.
mZRTS = (4x -14)
What is the value of x?
Answer:
x = 26
Step-by-step explanation:
m<RTS = 4x - 14 (given)
Based on the inscribed angle theorem, the measure of the inscribed angle in a semicircle = right angle (90°)
Therefore,
4x - 14 = 90
4x - 14 + 14 = 90 + 14 (addition property of equality)
4x = 104
4x/4 = 104/4
x = 26